Nodal analysis worksheet with answers

Free printable Nodal analysis worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
R1​ = 6 Ω+−V1​15 VR2​4 ΩIR2​AIs​1 A

Use nodal analysis to find the current IR2 through R2 in the direction of the arrow.

V1 = 15 VIs = 1 AR1 = 6 ΩR2 = 4 Ω
IR2 = A
2.Easy
R1​4 Ω+−V1​12 VR2​12 Ω+−V2​12 VR3​5 Ω+−V3​15 VA

Three branches are connected between node A and ground, as shown. Use nodal analysis to find the node voltage VA.

V1 = 12 VR1 = 4 ΩV2 = 12 VR2 = 12 ΩV3 = 15 VR3 = 5 Ω
VA = V
3.Medium
−+Vs​ = 9 VIs​5 AAR1​10 ΩR2​20 ΩB

The voltage source Vₛ between A and B has its + terminal at B, so it makes VB − VA = Vₛ. Use nodal analysis with a supernode to find the node voltage VA (measured from ground).

Is = 5 AVs = 9 VR1 = 10 ΩR2 = 20 Ω
VA = V
4.Medium
R1​ = 12 ΩR3​ = 6 ΩIR3​+−V1​6 VR2​20 ΩAR4​20 ΩBIs​1.5 A

Use nodal analysis to find the current IR3 through R3 in the direction of the arrow.

V1 = 6 VIs = 1.5 AR1 = 12 ΩR2 = 20 ΩR3 = 6 ΩR4 = 20 Ω
IR3 = A
5.Hard
R1​ = 20 ΩR3​ = 10 Ω+−V1​9 VR2​8 ΩAR4​25 ΩBIs​?

The current source is adjusted until the node voltage at A is VA = 4.5 V. Use nodal analysis to find the source current Is (direction as shown).

V1 = 9 VR1 = 20 ΩR2 = 8 ΩR3 = 10 ΩR4 = 25 ΩVA = 4.5 V
Is = A
6.Hard
R1​ = 3 ΩR2​ = 30 ΩR4​ = 8 Ω+−V1​15 VR3​20 ΩAR5​20 ΩBIs​5 A−+V2​10 V

Use nodal analysis to find the node voltage VA (measured from ground).

V1 = 15 VIs = 5 AV2 = 10 VR1 = 3 ΩR2 = 30 ΩR3 = 20 ΩR4 = 8 ΩR5 = 20 Ω
VA = V

Answer key

  1. 1. IR2 = 0.9 A
  2. 2. VA = 13.13 V
  3. 3. VA = 30.33 V
  4. 4. IR3 = −0.7836 A
  5. 5. Is = 0.6525 A
  6. 6. VA = 13.61 V

Full step-by-step solutions: practise this topic on examproblems.com.